The image consists of multiple layers of circles in a hexagonal grid arrangement. The layer scaling factors are integer powers of the golden ratio. Seamless infinite zoom is achieved by gradually blending in / out the fine / large scale layers. Draw function draws a single animation frame:
Your posted animated GIF consists of 60 single frames, according to my Australian file manager, file size being 14MB woah. File seems attached to forum. I had thought that file size attachment limitation was 10MB.
for Abs[ds] > 3 the graphics from Draw[ds] is uniformly black. An infinite zoom cannot be directly observed. The pictures for ds \in \{-1,1,1\} seem to agree visually. How did ds vary in the GIF animation?
Background: I’m interested in a working example of a fractal one can zoom out, with other words iterate backwards behind the starting set or with again other words having the starting set appearing if iterating from negative iteration numbers to iteration number 0. Then going forward, i.e. zoom in. Your example seemed to deliver it, but seems to need some more work to accomplish that.
Hey! Thats amazing! Yeah the hexagon represents an elementary part of our nature, you can find it almost everywhere, in the eyes of bees, even on saturn (the 6th Planet) ^^ and in all what is elementary for life like carbon, here a example from a carbon molecule, recorded with a atomic force microscope (atomic/scanning force microscope, AFM) in the IBM research center in zurich.
Forgot to mention, ds varies from 0 to 1. It is the fractional part of the scale exponents, so when it reaches 1 we have the same set of scales and a perfect loop. If there was an infinite number of layers, we could change ds from -inf to +inf.
